The results of studies of the transport of thermal frequency phonons in amorphous dielectrics (glasses and glass-like materials) are presented. It is shown that the formation of a plateau region in the temperature dependence of thermal conductivity at T < 10 K can be associated with the appearance of a “gap” in the spectrum of phonon states. The features of the transport characteristics of phonons in single crystals of solid solutions of aluminum-rare-earth garnets (ARGs) are analyzed in the helium temperature range in the presence of low-energy excitations of a paramagnetic nature. It is shown that under the conditions of a non-stationary process of propagation of a thermal pulse at a given thermostat temperature, it is possible to establish equilibrium in the system of nonequilibrium phonons-two-level systems (TLSs) in a sample of a certain length. It has been found that the efficiency of interaction of phonons with TLSs and their transport depend on the type, magnetic moment of the rare-earth ion, energy, and spectral features in the ARG lattice.

介绍了热频率声子在非晶电介质（玻璃和类玻璃材料）中传输的研究结果。结果表明，在T处热导率的温度依赖性中形成平台区< 10 K 可能与声子态光谱中出现“间隙”有关。在氦温度范围内，在顺磁性的低能激发下，分析了铝稀土石榴石（ARG）固溶体单晶中声子的传输特性。结果表明，在给定恒温器温度下热脉冲传播的非平稳过程条件下，有可能在一个样品中的非平衡声子-双能级系统（TLS）系统中建立平衡。一定的长度。已经发现，声子与 TLS 的相互作用效率及其传输取决于稀土离子的类型、磁矩、能量和 ARG 晶格中的光谱特征。